/usr/share/octave/packages/control-3.0.0/lyap.m is in octave-control 3.0.0-2.
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##
## This file is part of LTI Syncope.
##
## LTI Syncope is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## LTI Syncope is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with LTI Syncope. If not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn{Function File} {@var{x} =} lyap (@var{a}, @var{b})
## @deftypefnx{Function File} {@var{x} =} lyap (@var{a}, @var{b}, @var{c})
## @deftypefnx{Function File} {@var{x} =} lyap (@var{a}, @var{b}, @var{[]}, @var{e})
## Solve continuous-time Lyapunov or Sylvester equations.
##
## @strong{Equations}
## @example
## @group
## AX + XA' + B = 0 (Lyapunov Equation)
##
## AX + XB + C = 0 (Sylvester Equation)
##
## AXE' + EXA' + B = 0 (Generalized Lyapunov Equation)
## @end group
## @end example
##
## @strong{Algorithm}@*
## Uses SLICOT SB03MD, SB04MD and SG03AD by courtesy of
## @uref{http://www.slicot.org, NICONET e.V.}
##
## @seealso{lyapchol, dlyap, dlyapchol}
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: January 2010
## Version: 0.2.1
function [x, scale] = lyap (a, b, c, e)
scale = 1;
switch (nargin)
case 2 # Lyapunov equation
if (! is_real_square_matrix (a, b))
## error ("lyap: a, b must be real and square");
error ("lyap: %s, %s must be real and square", ...
inputname (1), inputname (2));
endif
if (rows (a) != rows (b))
## error ("lyap: a, b must have the same number of rows");
error ("lyap: %s, %s must have the same number of rows", ...
inputname (1), inputname (2));
endif
[x, scale] = __sl_sb03md__ (a, -b, false); # AX + XA' = -B
## x /= scale; # 0 < scale <= 1
case 3 # Sylvester equation
if (! is_real_square_matrix (a, b))
## error ("lyap: a, b must be real and square");
error ("lyap: %s, %s must be real and square", ...
inputname (1), inputname (2));
endif
if (! is_real_matrix (c) || rows (c) != rows (a) || columns (c) != columns (b))
## error ("lyap: c must be a real (%dx%d) matrix", rows (a), columns (b));
error ("lyap: %s must be a real (%dx%d) matrix", ...
rows (a), columns (b), inputname (3));
endif
x = __sl_sb04md__ (a, b, -c); # AX + XB = -C
case 4 # generalized Lyapunov equation
if (! isempty (c))
print_usage ();
endif
if (! is_real_square_matrix (a, b, e))
## error ("lyap: a, b, e must be real and square");
error ("lyap: %s, %s, %s must be real and square", ...
inputname (1), inputname (2), inputname (4));
endif
if (rows (b) != rows (a) || rows (e) != rows (a))
## error ("lyap: a, b, e must have the same number of rows");
error ("lyap: %s, %s, %s must have the same number of rows", ...
inputname (1), inputname (2), inputname (4));
endif
if (! issymmetric (b))
## error ("lyap: b must be symmetric");
error ("lyap: %s must be symmetric", ...
inputname (2));
endif
[x, scale] = __sl_sg03ad__ (a, e, -b, false); # AXE' + EXA' = -B
## x /= scale; # 0 < scale <= 1
otherwise
print_usage ();
endswitch
if (scale < 1)
warning ("lyap: solution scaled by %g to prevent overflow", scale);
endif
endfunction
## Lyapunov
%!shared X, X_exp
%! A = [1, 2; -3, -4];
%! Q = [3, 1; 1, 1];
%! X = lyap (A, Q);
%! X_exp = [ 6.1667, -3.8333;
%! -3.8333, 3.0000];
%!assert (X, X_exp, 1e-4);
## Sylvester
%!shared X, X_exp
%! A = [2.0 1.0 3.0
%! 0.0 2.0 1.0
%! 6.0 1.0 2.0];
%!
%! B = [2.0 1.0
%! 1.0 6.0];
%!
%! C = [2.0 1.0
%! 1.0 4.0
%! 0.0 5.0];
%!
%! X = lyap (A, B, -C);
%!
%! X_exp = [-2.7685 0.5498
%! -1.0531 0.6865
%! 4.5257 -0.4389];
%!
%!assert (X, X_exp, 1e-4);
## Generalized Lyapunov
%!shared X, X_exp
%! A = [ 3.0 1.0 1.0
%! 1.0 3.0 0.0
%! 1.0 0.0 2.0];
%!
%! E = [ 1.0 3.0 0.0
%! 3.0 2.0 1.0
%! 1.0 0.0 1.0];
%!
%! B = [-64.0 -73.0 -28.0
%! -73.0 -70.0 -25.0
%! -28.0 -25.0 -18.0];
%!
%! X = lyap (A.', -B, [], E.');
%!
%! X_exp = [-2.0000 -1.0000 0.0000
%! -1.0000 -3.0000 -1.0000
%! 0.0000 -1.0000 -3.0000];
%!
%!assert (X, X_exp, 1e-4);
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